The intention of this project is to write a simple Particle-Mesh gravitational simulation that allows us to simulate the motion of N bodies. This consists of four applications: TestSimulation, BenchmarkSimulation, NBody_Comparison and NBody_Visualiser.

This project is compiled using CMake so compiling requires cmake version 3.16 and C++17 at a minimum.

In the same level in the directory as this README.md file, run cmake -B build to configure the project and create the build directory. To compile the programs run cmake --build build. Now you should be able to find TestSimulation, BenchmarkSimulation, NBody_Comparison and NBody_Visualiser in the /build/bin/ folders. To run a program type ./build/bin/{program_name}. TestSimulation just contains unit tests for the different functions, classes and algorithms used in this project and BenchmarkSimulation contains code to print out benchmark times for different functions using different numbers of threads.

This application is built to generate a cubic grid with periodic boundary conditions of length $n_c$ with total number of cells $N_c$ and then generate an amount of particles $n_p$ determined by a user given average number of particles per cell value. The particle mesh method is then used to calculate a graviation field in this grid given a box length and an expansion factor is applied to the box to simulate an expanding universe. This program can be run using a command similar to the one shown below:

./build/bin/NBody_Visualiser -nc 101.0 -np 12 -t 1.5 -dt 0.01 -F 1.02 -o Images -s 42

The flag -h when used displays a help message shows run instructions an explains the required flags used to run the program. All the flags are required and no optional commands exist. -s is the random seed that is used with the std::default_random_engine generator from the STL <random> library in c++. -o is the output folder that is the images are outputted time. -F is the factor by which the box is scaled with, -dt is the time-step for each iteration in the simulation and -t is the total time elapsed.

This program visualises a developing universe through modelling the graviational fields of multiple particles with the same mass using the particle mesh method.

Brief instructions can be found below.
Usage: NBody_Visualiser -nc <number_of_cells> -np <average_particles_per_cell> -t <total_time> -dt <time_step> -F <expansion_factor> -o <output_folder> -s <random_seed>
Options:
  -h                                       Show this help message
  -nc <number_of_cells>                    Number of cells wide the equal sided box has
  -np <average_particles_per_cell>         Average number of particles each cell has
  -t  <total_time>                         Total time the simulation will run for
  -dt <time_step>                          Amount of time that is incremented each propagation
  -F  <expansion_factor>                   Factor that the absolute value of the box expands
  -o  <output_folder>                      Folder that output images are sent to
  -s  <random_seed>                        Seed that is used to generate initial randomised positions

This will then output .pbm images to the directory <output_folder>/<seed>/<Expansion_Factor>/. It should be noted that all values that are used in naming conventions that are not restricted to integers will that at least a decimal . following the number even if it is whole. The file naming convention is UniverseSim_dt_<time_step>_time_<current_time_simulation>_num_cells_<number_of_cells>_ppc_<average_particles_per_cell>.pbm where <current-time_simulation> is the value of the time at the timestep the image of the particle density distribution was captured at.

This application runs $x$ different simulations in parallel using distributed memory and then outputs radial correlation statistics of said simulations to a user specified folder in .csv format. Each simulation is ran with a different expansion factor. The user needs to input four arguments: The number of simulations $x$, the output folder that the results are saved to, the maximum expansion factor and the minimum expansion factor. The $x$ simulations are generated with expansion equally spaced expansion factors that range between the maximum and minimum ones specified. The program can be run using the below command format:

mpirun -np <number_simulations> ./build/bin/NBody_Comparison -o <output_folder> -emin <minimum_expansion_factor> -emax <maximum_expansion_factor>

mpirun -np 4 ./build/bin/NBody_Comparison -o Correlation -emin 1 -emax 1.04

Here mpirun is used to distribute the program across the specified nodes in order to commence the parallel computation. The -np flag is used to specify the number of parallel proccesses that will be used to run independent simulations. The -o flag is used to specify the output folder that the binned radial correlations will be outputted to, the -emin flag is used to specify the minimum expansion factor that will be used and -emax represents the maximum expansion factor.

The file naming convention of the output .csv file is Comparison_<number_simulations>_<minimum_expansion_factor>_<maximum_expansion_factor>.csv.